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Turbulent buoyant jets are a major feature in fire hazards. The solution of the Reynolds Averaged Navier-Stokes (RANS) equations through computational fluid dynamic (CFD) techniques allow such flows to be simulated. The use of Reynolds averaging requires an empirical model to close the set of equations, this is known as the turbulence model. This thesis undertakes to investigate linear and nonlinear approaches to turbulence modelling and to apply the knowledge gained to the simulation of compartment fires. The principle contribution of this work is the reanalysis of the standard k- ε turbulence model and the implementation and application of more sophisticated models as applied to thermal plumes. Validation in this work, of the standard k- ε model against the most recent experimental data, counters the established view that the model is inadequate for the simulation of buoyant flows. Examination of previous experimental data suggests that the measurements were not taken in the self-similar region resulting in misleading comparisons with published numerical solutions. This is a significant conclusion that impacts of the general approach taken to modelling turbulence in this field. A number of methods for modelling the Reynolds stresses and the turbulent scalar fluxes have been considered and, in some cases for the first time, are applied to nonisothermal flows. The relative influence of each model has been assessed enabling its performance to be gauged. The results from this have made a valuable contribution to the knowledge in the field and have enabled the acquired experience to be applied to the simulation of compartment fires. The overall conclusion drawn from this thesis is that for the simulation of compartment fires, the most appropriate approach with current computational resources, is still the buoyancy corrected standard k- ε model. However, the turbulence scalar flux should be modelled by the generalised gradient diffusion hypothesis (GGDH) rather than the eddy-diffusivity assumption.